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Question
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.
Solution
It can be observed that 1 round of wire will cover 3 mm height of cylinder.
Number of rounds = Height of cylinder/Diameter of wire
= 12/0.3 = 40 rounds
Length of wire required in 1 round = Circumference of base of cylinder
= 2πr = 2π × 5 = 10π
Length of wire in 40 rounds = 40 × 10π
`= (400xx22)/7 = 8800/7`
= 1257.14 cm = 12.57 m
Radius of wire = 0.3/2 = 0.15 cm
Volume of wire = Area of cross-section of wire × Length of wire
= π(0.15)2 × 1257.14
= 88.898 cm3
Mass = Volume × Density
= 88.898 × 8.88
= 789.41 gm
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